3. The number of mahjong games played in a given family on the Lunar New Year can be modeled as a Geometric() random variable, where the value of the parameter varies from family to family. Assume a Uniform(0, 1) prior on . (a) Suppose Bob's family played x₁ games on the 2020 festival, x2 games in 2019, up to xt games t years ago. Show that the posterior is a Beta(a, 3) random variable. What are a and B? (b) Bob observed that x₁ = 22 and 2 = 41. What is the expected number of games that his family will play this year?
3. The number of mahjong games played in a given family on the Lunar New Year can be modeled as a Geometric() random variable, where the value of the parameter varies from family to family. Assume a Uniform(0, 1) prior on . (a) Suppose Bob's family played x₁ games on the 2020 festival, x2 games in 2019, up to xt games t years ago. Show that the posterior is a Beta(a, 3) random variable. What are a and B? (b) Bob observed that x₁ = 22 and 2 = 41. What is the expected number of games that his family will play this year?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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Transcribed Image Text:3. The number of mahjong games played in a given family on the Lunar New Year can be
modeled as a Geometric (0) random variable, where the value of the parameter varies from
family to family. Assume a Uniform (0, 1) prior on 0.
(a) Suppose Bob's family played x₁ games on the 2020 festival, x2 games in 2019, up to xt
games t years ago. Show that the posterior is a Beta(a, ß) random variable. What are
a and 3?
(b) Bob observed that x₁
22 and x₂ = 41. What is the expected number of games that
his family will play this year?
-
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